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A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

A) 1/4 B) 1/2

C) 3/4 D) 7/12

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A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

Answer: C) 3/4

Explanation:

Let A, B, C be the respective events of solving the problem and A , B, CA , B, C be the respective events of not solving the problem. Then A, B, C are independent event

A, B, C∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 P(A)=12, P(B)=23, P(C)= 34PA=12, PB=23, PC= 34

 P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = P(ABC)PA∩B∩C 

                  = P(A)P(B)P(C)PAPBPC         [ A, B, C are Independent]∵ A, B, C are Independent                       

                  =  12×23×3412×23×34  

                  = 1414  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1141-143/4

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